1. Photons: Light Waves Behaving as Particles
Chapter 38
Photons: Light Waves Behaving as Particles
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2. Learning Goals for Chapter 38
Looking forward at …
how Einstein’s photon picture of light explains the photoelectric effect.
how experiments with x-ray production provided evidence that light is emitted in the form of photons.
how the scattering of gamma rays helped confirm the photon picture of light.
how the Heisenberg uncertainty principle imposes fundamental limits on what can be measured.
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3. Introduction
This plastic surgeon is using two light sources: a headlamp that emits a beam of visible light and a handheld laser that emits infrared light.
The light from both sources is emitted in the form of packets of energy called photons.
The individual photons in the infrared laser are actually less energetic than the photons in the visible light.
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4. The photoelectric effect
To escape from the surface, an electron must absorb enough energy from the incident light to overcome the attraction of positive ions in the material.
These attractions constitute a potential-energy barrier; the light supplies the “kick” that enables the electron to escape.
The ejected electrons form what is called a photocurrent.
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5. The photoelectric effect: Experimental results
The photocurrent depends on the light frequency. For a given material, monochromatic light with a frequency below a minimum threshold frequency produces no photocurrent, regardless of intensity.
There is no measurable time delay between when the light is turned on and when the cathode emits photoelectrons (assuming the frequency of the light exceeds the threshold frequency). This is true no matter how faint the light is.
The stopping potential does not depend on intensity, but does depend on frequency. The only effect of increasing the intensity is to increase the number of electrons per second and hence the photocurrent i. The greater the light frequency, the higher the energy of the ejected photoelectrons.
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6. Photocurrent in the photoelectric effect
Shown are graphs of photocurrent as a function of potential difference VAC for light of a given frequency and two different intensities.
The reverse potential difference −V0 needed to reduce the current to zero is the same for both intensities.
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7. Einstein’s photon explanation
Einstein made the radical postulate that a beam of light consists of small packages of energy called photons or quanta.
The energy of an individual photon is:
Here Planck’s constant is h = × 10−34 J ∙ s
An individual photon arriving at a surface is absorbed by a single electron.
The electron can escape from the surface only if the energy it acquires is greater than the work function ϕ.
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8. Einstein’s explanation of the photoelectric effect
This explains how the energy of an emitted electron in the photoelectric effect depends on the frequency of light used.
The greater the work function of a particular material, the higher the minimum frequency needed to emit photoelectrons.
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9. Table 38.1: Work functions of several elements
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10. Photon momentum Every particle that has energy must have momentum.
Photons have zero rest mass, and a particle with zero rest mass and energy E has momentum with magnitude p given by E = pc [see Chapter 37 on Relativity].
Thus the magnitude p of the momentum of a photon is:
The direction of the photon’s momentum is simply the direction in which the electromagnetic wave is moving.
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11. X-ray production
Shown is an experimental arrangement for making x rays.
The next slide shows the resulting x-ray spectrum.
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12. X-ray production
The greater the kinetic energy of the electrons that strike the anode, the shorter the minimum wavelength of the x rays emitted by the anode.
The photon model explains this behavior.
Higher-energy electrons can convert their energy into higher-energy photons, which have a shorter wavelength.
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13. X-ray absorption and medical imaging
Atomic electrons can absorb x rays.
Hence materials with many electrons per atom tend to be better x-ray absorbers than materials with few electrons.
Bones contain large amounts of elements such as phosphorus and calcium, with 15 and 20 electrons per atom, respectively.
In soft tissue, the predominant elements are hydrogen, carbon, and oxygen, with only 1, 6, and 8 electrons per atom, respectively.
Hence x rays are absorbed by bone but pass relatively easily through soft tissue.
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14. X-ray scattering: The Compton experiment
In the Compton experiment, x rays are scattered from electrons.
The scattered x rays have a longer wavelength than the incident x rays, and the scattered wavelength depends on the scattering angle .
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15. Compton scattering
In Compton scattering, an incident photon collides with an electron that is initially at rest.
The photon gives up part of its energy and momentum to the electron, which recoils as a result of this impact.
The scattered photon flies off at an angle ϕ with respect to the incident direction, but it has less energy and less momentum than the incident photon.
Therefore, the wavelength of the scattered photon λ' is longer than the wavelength λ of the incident photon.
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16. Pair production
When gamma rays of sufficiently short wavelength are fired into a metal plate, they can convert into an electron and a positron, each of mass m and rest energy mc2.
The photon model explains this: The photon wavelength must be so short that the photon energy is at least 2mc2.
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17. Diffraction and uncertainty
When a photon passes through a narrow slit, its momentum becomes uncertain and the photon can deflect to either side.
A diffraction pattern is the result of many photons hitting the screen.
The pattern appears even if only one photon is present at a time in the experiment.
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18. Diffraction and uncertainty
These images record the positions where individual photons in a two-slit interference experiment strike the screen.
As more photons reach the screen, a recognizable interference pattern appears.
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19. The Heisenberg uncertainty principle
You cannot simultaneously know the position and momentum of a photon, or any other particle, with arbitrarily great precision.
The better you know the value of one quantity, the less well you know the value of the other.
There is a similar uncertainty relationship for the y- and z- coordinate axes and their corresponding momentum components.
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20. The Heisenberg uncertainty principle
Shown is a graphical representation of the Heisenberg uncertainty principle.
A measurement with uncertainties whose product puts them to the left of or below the blue line is not possible to make.
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21. Uncertainty in energy
There is also an uncertainty principle that involves energy and time.
The better we know a photon’s energy, the less certain we are of when we will observe the photon:
This relation holds true for other kinds of particles as well.
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